## How Many Triangles?

2016-09-22 19:09
The following problem was at a 2016 entrance test for the MIT PRIMES STEP program. I drew several triangles on a piece of paper. First I showed the paper to Lev and asked him how many triang… Read More

## Should You Apply To PRIMES?

2016-09-10 23:00
If you are a high-school student who wants to conduct research in mathematics, you should check out the MIT PRIMES program. If you enjoy solving the problems in our entrance test, that&rsquo&hell…Read More

## Alexander Shapovalov Crosses A River

2016-09-07 21:33
Alexander Shapovalov is a prolific puzzle writer. He has a special webpage of his river-crossing puzzles (in Russian). Here is one of these puzzles. Three swindlers have two suitcases each… Read More

## 3-Pile Nim As An Automaton

2016-08-09 23:02
In my paper with Joshua Xiong, Nim Fractals, we produced a bijection between P-positions in the three-pile Nim and a three-branch Ulam-Warburton automaton. We also defined a parent-child rel… Read More

## The Longest Optimal Game Of Nim

2016-08-07 18:18
In the game of Nim you have several piles with tokens. Players take turns taking several tokens from one pile. The person who takes the last token wins. The strategy of this game is well-kno… Read More

## Replace Question Marks

2016-08-07 00:02
Replace question marks with letters in the following sequence: Y, Y, ?, ?, Y, ?, Y, ?, R, R, R, R. Share: Read More

## Geometry Puzzles From The 35-th Lomonosov Tournament

2016-07-30 22:24
Problem 1. It is true that it is possible to put positive numbers at the vertices of a triangle so that the sum of two numbers at the ends of each side is equal to the length of the side? Th… Read More

## Your Deal Is Better Than My Deal

2016-06-12 19:12
Do you know how to cut a cake? I mean, mathematically. There is a whole area of mathematics that studies cake cutting. Mathematicians usually assume that each person has their own idea of wh… Read More

## The Reuleaux Tetrahedron

2016-06-04 23:08
Why are manhole covers round? The manhole covers are round because the manholes are round. Duh! But the cute mathematical answer is that the round shapes are better than many other shapes be… Read More

## Who Is Guilty?

2016-06-04 22:07
I am running a PRIMES-STEP program for middle school students, where we try to do research in mathematics. In the fall of 2015 we decided to study the following topic in logic. Suppose there… Read More

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